Bidirectional model transformation (BX) plays a vital role in Model-Driven Engineering.
A major challenge in conventional \emph{relational} and \emph{bidirectionalization}-based BX approaches is the ambiguity issue, i.e., the backward transformation may not be uniquely determined by the consistency relation or the forward transformation.
A promising solution to the ambiguity issue is to adopt \emph{putback}-based bidirectional programming, which realizes a BX by specifying the backward transformation.
However, existing \emph{putback}-based approaches do not support multiple conversions of the same node (namely a shared node).
Since a model is a graph, shared nodes are very common and inevitable.
Consequently, existing \emph{putback}-based approaches cannot be directly applied to bidirectional model transformation.
This paper proposes a novel approach to BX.
We define a new model-merging-based BX combinator, which can combine two BXs owning shared nodes into a well behaved composite BX.
Afterwards, we propose a \emph{putback}-based BX language XMU to address the ambiguity issue, which is built on the model-merging-based BX combinator.
We present the formal semantics of XMU which can be proven well behaved.
Finally, a tool support is also introduced to illustrate the usefulness of our approach.